The Irascible Professor
SMIrreverent Commentary
on the State of Education in America Today

by Dr. Mark H. Shapiro

"Do
not worry about your difficulties in Mathematics. I can assure you mine
are still greater." ... ... Albert Einstein.

Commentary
of the Day - December 21, 2005: Great Expectations. Guest commentary
by Poor Elijah (Peter Berger).

Nearly twenty
years ago a movie about math class won an Oscar nomination. Stand
and Deliver told the story of a room full of poor, mostly Hispanic
potential dropouts and their teacher, Jaime Escalante. In the film
Mr. Escalante's high school students progressed from not knowing arithmetic
to mastering calculus in a single term, largely because he expected great
things of them.

In real life it
didn't happen that way. Mr. Escalante spent over a decade building
his math program, including a sequence of feeder courses beginning in junior
high. The real kids who made it through his high-flying calculus
class worked for years to get there.

Expectations are
important. Some students never get a chance to attempt rigorous coursework
because they're constrained by stereotypes rooted in race and poverty,
what former Education Secretary Rod Paige termed "the soft bigotry of low
expectations." At the same time, many poor, minority students bring
significant disadvantages from home, which genuinely limit their prospects
for success at school. In addition, for thirty years the education
reform movement has instituted low expectations for all races, colors,
and classes.

Schools, like
any enterprise, need to shed faulty assumptions. The persistent issues
of race and poverty merit our attention as a nation. But Mr. Escalante's
students didn't go from zero to calculus after a period of simply
believing in themselves. It took years of individual commitment and
toil.

Believing in yourself,
especially in the absence of actually having to do anything, is relatively
easy. In fact, thanks to our national self-esteem crusade, American
kids score quite well when it comes to believing in themselves. In
a 1992 analysis of Asian and American math students, for instance, American
students ranked highest when it came to expressing confidence in their
math abilities. Unfortunately, American math students ranked lowest when
it came to actual "mathematical competence." In other words, American
kids think highly of themselves as math students, despite the fact that
they aren't very good at mathematics.

More alarming
still, it's likely that they don't know much math in part precisely because
they've been encouraged to think so highly of themselves. The same
study reported that most American teachers value sensitivity to their students
above clarity of instruction. In contrast, Asian teachers are more
concerned with clearly presenting subject matter. American teachers,
worried about damaging self-esteem, tended to gloss over students' errors,
while their Asian colleagues didn't shy away from their students' mistakes
and instead pointedly examined them as part of the learning process.

You can't blame
our national math mediocrity solely on the cult of self-esteem. Over
the past few decades, the decades that have seen the decline in achievement
that everybody's talking about, reformers have replaced more traditional
programs that build on fundamentals with approaches that sideline the basics
in favor of "higher order" math and "problem solving." These innovations,
nicknamed "fuzzy math" by critics, are responsible as well. In the
same way, whole language, another touted reform, is culpable for many American
students' inability to read.

The merits of
these instructional methods, and their defects, are worth discussing.
But beyond debating the efficacy of one math program over another, we need
to confront a more worrisome question. Why have schools found fuzzy
math, or fuzzy anything, so appealing?

Why are the multiplication
tables passé? Why do experts disdain memorization? Why
did schools relegate phonics to the ash heap? How did content become
a dirty word? Why did we banish facts from history classes and textbooks
from science courses? When did "How do you feel about that?" become
the central question in American classrooms?

Reformers recite
a familiar litany of reasons, from "engaging" students to developing "higher
order" skills for the twenty-first century. But these justifications
are smoke screens. Logic and creativity are neither new nor more
necessary in this century than they were in the last. And not everything
we need to do and learn in this life is engaging. Some of it's pure
drudgery; but, that's hardly an excuse not to do it.

We stopped doing
and learning a lot of things in school because they weren't fun.

Experts justify
calculators on the grounds that it's more important for students to focus
on those higher order skills. That's true if you're talking about
high school math or physics. But it's not the reason we're handing
out calculators to nine-year-olds. The real reason is memorizing
addition facts and the multiplication tables is a pain in the neck.
Requiring that kids learn the basics and practice their skills might make
them not enjoy math. We don't want that to happen, so instead we
deny them those skills, which means they can't do math.

Experts point
out that poor, minority students lack the basic skills and learning foundation
that middle class kids are more likely to acquire at home. While
they're sadly overstating how many middle class kids come to school with
those advantages anymore, growing up middle class clearly conveys learning
benefits.

These same experts
are also quick to insist that poor, minority students need college prep
courses like algebra, trig, and Mr. Escalante's calculus. The trouble
is their solution to lacking the basics is to skip them in the name of
social equality and jump right to the flashy stuff. This is exactly
the wrong approach.

All students need
to master the fundamentals. Kids who start out at a deficit are precisely
the kids who need them the most. The less familiar you are with the
basics, the more time, not the less time, you need to spend on them.

Despite all the
rhetoric and good intentions, there's nothing that schools can do to eliminate
hardships at home or even to substantially compensate for them. Starting
out behind necessarily means you have further to go to catch up.

There is no shortcut
to learning. That's the expectation we need to pass on to all students,
whether they like it or not.

The
IP comments: The IP agrees only in part with Poor Elijah's comments.
The IP was lucky enough to have gone through elementary school in Cambridge,
MA in the late forties and fifties, well before the self-esteem movement
took hold. We slogged our way through the multiplication tables,
learned long division, how to take square roots by hand, and all that.
But, in truth, the level of mathematics teaching and learning really wasn't
all that much better than it is today. The reason for that was that
most of the IP's elementary school teachers knew very little mathematics
themselves. They viewed elementary mathematics as a set of facts
to be memorized, rather than as a set of logical procedures. We memorized
the multiplication tables, and rules for multiplying and dividing fractions.
However, we did not learn why those rules worked. Our teachers had
never studied the axioms of arithmetic, so they were about as clueless
as their students when it came to the why of arithmetic. In
the intervening years it seems that students not only don't learn the why
of elementary mathematics, they also don't learn the what.
In recent years, the National
Council of Teachers of Mathematics (NCTM) has tried to introduce more
of the why into school mathematics; however, they too often have
succumbed to the excess emphasis on constructivist teaching that prevails
today and a desire to avoid the unpleasant realities of associated with
learning the what of school math. For better or worse, the
what and the why of elementary mathematics are inextricably
connected. And, one can't really learn one without also learning
the other.